System and method for mode-based multi-hypothesis tracking using parametric contours

ABSTRACT

A system and method for object tracking using probabilistic mode-based multi-hypothesis tracking (MHT) provides for robust and computationally efficient tracking of moving objects such as heads and faces in complex environments. A mode-based multi-hypothesis tracker uses modes that are local maximums which are refined from initial samples in a parametric state space. Because the modes are highly representative, the mode-based multi-hypothesis tracker effectively models non-linear probabilistic distributions using a small number of hypotheses. Real-time tracking performance is achieved by using a parametric causal contour model to refine initial contours to nearby modes. In addition, one common drawback of conventional MHT schemes, i.e., producing only maximum likelihood estimates instead of a desired posterior probability distribution, is addressed by introducing an importance sampling framework into MHT, and estimating the posterior probability distribution from the importance function.

BACKGROUND

1. Technical Field

The invention is related to a system for tracking objects, and inparticular, to a system and method for real-time probabilisticmode-based multi-hypothesis tracking using parametric causal contourmodels.

2. Related Art

Accurate tracking of the objects, such as, for example, the human headand face is an important application of object tracking. For example,the ability to track moving people in video surveillance and videoconferencing systems greatly increases the utility of such systems.Unfortunately, robust and efficient tracking of human heads and faces incomplex environments is a problem which has not been adequatelyaddressed by existing tracking schemes.

In general, the basic objective of most conventional tracking schemes isto accurately and efficiently compute a posterior probability of atracking state for a target object or objects with respect to an imageobservation. With respect to heads and faces, the tracking statetypically represents information such as, for example, location andorientation of the head or face. Given this basic objective, there arethree general approaches to estimating a probability distribution, i.e.,pure parametric, pure non-parametric and semi-parametric.

The well-known Kalman filter is a good example of the pure parametricapproach, where the distribution is assumed to be Gaussian.Unfortunately, because of its uni-mode assumption, the use of Kalmanfilters has only achieved limited success in real-world trackingapplications. To overcome this difficulty, one conventional scheme usesa non-parametric approach wherein the object tracking probabilitydistribution is represented and estimated by a set of properlypositioned and weighted “particles.” The scheme works with bothmulti-mode distributions and non-linear dynamic systems. However, aswith most if not all non-parametric algorithms, this scheme requires alarge number of particles. Further, the required number of particlesgrows exponentially with the dimensionality of the state space.Unfortunately, as the number of particles increases, so does thecomputational complexity and cost of solving the tracking problem.

Several other conventional schemes have attempted to address the problemof needing large numbers of particles for tracking by simply making theparticles more effective. For example, one such scheme uses an annealedparticle filter for tracking an articulated human figure. This scheme isbased on probabilistic pruning, and focuses its particles in aneighborhood around global peaks of the weighting function. While thisscheme greatly reduces the number of particles needed, it achieves thisresult at the cost of sacrificing robustness in a Bayesian framework. Inparticular, by discarding inferior peaks in the weighting function, thisscheme can lose the true state of the object being tracked when largedistractions or discontinuities occur in the observation data.

Several other conventional schemes have attempted to address the problemof needing large numbers of particles for tracking by using asemi-parametric approach where the probability distribution to beestimated is modeled by a mixture of parametric distributions. Thesesemi-parametric approaches retain the capability of representingmulti-mode distributions, but with much fewer samples or particles. Inparticular, one of the most successful semi-parametric schemes used inobject tracking is known as multi-hypothesis tracking (MHT).

MHT was first developed in radar-tracking systems. However, oneconventional scheme has successfully applied MHT in articulated humanbody tracking. MHT works in a parametric state space. Each hypothesis isa particular configuration of parameters in the state space, and theoverall state is represented by a mixture of multiple hypotheses. Onelimitation with the classic MHT, as used in radar tracking, is that itassumes that a set of discrete hypotheses is available at any time step.This assumption is valid in radar tracking where the goal is toassociate multiple detected targets with multiple airplanes, missiles,spacecraft, etc. However, in visual tracking, this assumption cannoteasily be met. For example, for human head tracking, it would beextremely difficult to develop a single high-level “feature detector”that can detect a set of discrete hypotheses of the head position/poseat every frame. On the other hand, using low-level features such asimage edges in this scheme quickly leads to an intractable number ofhypotheses.

Another conventional scheme addresses this particular difficulty byfirst using an appearance-based gradient local search to generate a setof hypotheses (local maximums), and then constructing a likelihoodfunction as a piecewise Gaussian by combining the multiple hypotheses.While this approach has successfully demonstrated the effectiveness ofthe MHT paradigm in visual tracking, it has three major difficulties.First, for visual tracking, the appearance or template-based approachesonly work with relatively rigid objects and with objects that rarelychange orientation and intensity. For head tracking, however, the headorientation and environmental lighting can change from frame to frame,causing head appearance change dramatically. Second, this scheme uses aniterative Gauss-Newton method to generate hypotheses, which is bothcomputationally expensive and unsuitable for real-time tracking.Finally, and most importantly, while this scheme produces maximumlikelihood estimates, it does not compute the posterior probability ofthe tracking state with respect to the image observation. As a result,the tracking performance of this scheme can be significantly degraded.

Therefore, what is needed is a system and method for tracking objectssuch as heads and faces that is both robust in complex environments andcomputationally efficient. Further, this system and method should becapable of tracking objects wherein the appearance is capable ofchanging from one image frame to the next. In addition, this system andmethod should be capable of using multi-hypothesis tracking while alsocomputing a posterior probability of the tracking state with respect toimage observations.

SUMMARY

A system and method for object tracking as described herein solves theaforementioned problems, as well as other problems that will becomeapparent from an understanding of the following description by providinga novel probabilistic mode-based multi-hypothesis tracking (MHT) systemfor tracking moving objects. A mode-based multi-hypothesis tracker, asdescribed herein, is both robust in complex environments, such as, forexample, cluttered backgrounds, partial occlusion, and changing lightingconditions, and computationally efficient. Further, the mode-basedmulti-hypothesis tracker is capable of tracking any object that can bemodeled using parametric contours. For example, objects that can bemodeled using parametric contours include vehicles, such as cars,aircraft, missiles, boats, etc., animals, people, including the heads,faces, arms legs, hands and fingers of those people, or any other objectthan can be modeled using parametric contours. It should be noted thatfor purposes of explanation, the mode-based multi-hypothesis tracker isdescribed herein with respect to tracking of human heads and faces, butthat the techniques described are equally applicable to tracking anyother desired object.

Note that the following discussion makes use of the terms “sample” and“mode.” In the context of the following discussion, “sample” is used todenote a state space configuration obtained from some prior distributionor prediction scheme. “Mode” is used to denote a refined “sample” thatcorresponds to a local maximum in the distribution. Note that both“sample” and “mode” represent a particular configuration of parametersin the state space.

In general, unlike conventional MHT schemes, the mode-basedmulti-hypothesis tracker described herein uses parametric contours,instead of object appearance, to model an object of interest. This isparticularly effective in head tracking, where the head can beeffectively modeled by a parametric ellipse. While the head orientationand lighting can dramatically change the head appearance, the contour ofthe head remains approximately the same shape. Further, in oneembodiment, computationally efficient real-time tracking capability isachieved through the use of a novel causal contour model which avoidsthe necessity of iterative model refinement. Finally, the capability tocompute a posterior probability of the tracking state X_(t) with respectan image observation Z_(t) at time t, is added to MHT by placing the MHTtechnique into an importance sampling framework so as to effectivelyestimate the desired posterior p(X_(t)|Z_(t)).

Specifically, the mode-based multi-hypothesis tracker tracks at leastone object through a sequence of images. The assumption is made that inthe first frame, the location and contour of the object or objects isknown to the mode-based multi-hypothesis tracker. In other words, a“sample” denoting a particular state space configuration obtained from aprior distribution or prediction scheme is known with respect to thefirst frame. Any of a number of conventional techniques is used tolocate the object in the initial image frame. For example, suchtechniques include edge detection, the use of color or intensitygradients, manual identification of the initial location, or any otherconventional prior distribution or prediction scheme. The mode-basedmulti-hypothesis tracker then tracks the object or objects throughoutthe remaining sequence of images in the manner described below.

In particular, given the initial sample, a sequence of image frames isthen provided for processing by the mode-based multi-hypothesis tracker.Using this sample, the mode-based multi-hypothesis tracker thendetermines at least one corresponding mode for an input image frame. Inother words, given the initial sample, the mode-based multi-hypothesistracker determines one or more “modes” that correspond to local maximumsin the distribution. Finally, after determining the mode having thehighest estimated posterior p(X_(t)|Z_(t)), that mode is provided as thecurrent target estimate, and is then used as the “sample” for processingthe next sequential image.

In one embodiment, given an initial sample, a number of likely modes arefirst determined or “refined” from an image using a conventional “activecontour” technique by performing an iterative search in a 2D imageplane. Conventional active contour techniques provide a deformablecurve, or “snake”, which moves over an image while minimizing itspotential energy. The energy of a snake can in general be divided intoan “internal energy” term constraining the overall shape of the snake,and an “external energy” function provided by the image driving thesnake towards a desired boundary. With an appropriate image energyfunction and careful initialization, a snake can converge effectively tothe required boundary, thereby generating one or more modes.

Unfortunately, the modes returned by conventional active contourtechniques only represent maximum likelihood estimates as the activecontour technique converges on a target object boundary. Consequently,the mode-based multi-hypothesis tracker described herein expands on theconventional active contour technique by utilizing these modes togenerate an “importance sampling function.” Samples or “particles” arethen drawn from the importance function. Weights for these particles arethen computed. Finally, the weighted particles are then used forcomputing a posterior probability of a tracking state with respect to animage observation for each image frame.

While the aforementioned embodiment is useful for robust tracking ofobjects, it is not necessarily efficient enough to allow for real-timeobject tracking. Consequently, in another embodiment of the mode-basedmulti-hypothesis tracker, a 1D causal contour model is used in place ofthe iterative search of the 2D image plane to facilitate efficientsample refinement in identifying likely modes. As with the iterativesearch of the 2D image plane, the use of a 1D contour model foridentifying likely modes, is followed by the generation of an importancesampling function, weighting particles drawn from the importancefunction, and using the weighted particles for computing a posteriorprobability of a tracking state with respect to an image observation foreach image frame. One benefit of using the 1D causal contour model inplace of the iterative search of the 2D image plane is that imageprocessing speed in increased to the extent where real-time objecttracking is easily feasible on a typical PC-type computer.

Further, in still another embodiment, the robustness of the mode-basedmulti-hypothesis tracker is improved by a further refinement of thecontour model. In particular, the contour model, whether using a 2Dmodel, or the aforementioned 1D causal contour model, is further refinedby using a parametric contour as the state space so as to take domainknowledge such as a shape prior into account. Using parametric contoursin this manner serves to avoid or further reduce errors resulting frombackground distraction or discontinuities in the images. For example, inthe case of human head tracking, a parametric ellipse is used as the asthe state space. Clearly, parametric contours other than ellipses can beused, with the type of parametric contour being chosen that bestrepresents the object or objects being tracked in the images.

In view of the preceding discussion, it is clear that the mode-basedmulti-hypothesis tracker described herein is advantageous for use inreal-time tracking of any object which can be modeled using a parametriccontour. In addition to the just described benefits, other advantages ofthe mode-based multi-hypothesis tracker described herein will becomeapparent from the detailed description which follows hereinafter whentaken in conjunction with the accompanying drawing figures.

DESCRIPTION OF THE DRAWINGS

The specific features, aspects, and advantages of the present inventionwill become better understood with regard to the following description,appended claims, and accompanying drawings where:

FIG. 1 is a general system diagram depicting a general-purpose computingdevice constituting an exemplary system for using a mode-basedmulti-hypothesis tracker to track objects.

FIG. 2 illustrates an exemplary architectural diagram showing exemplaryprogram modules for using a mode-based multi-hypothesis tracker to trackobjects.

FIG. 3 illustrates an exemplary ID contour model as used by a mode-basedmulti-hypothesis tracker to track objects in an image frame.

FIG. 4A through FIG. 4C illustrate tracking of a human head in variousposes through a sequence of images using a mode-based multi-hypothesistracker with a fitted parametric ellipse.

FIG. 4D through FIG. 4F illustrate tracking of a human head in variousposes through a sequence of images using a mode-based multi-hypothesistracker with a fitted parametric ellipse, wherein the head being trackedis partially occluded by another human head.

FIG. 5A through FIG. 5C illustrate tracking of a human head in variousposes through a sequence of images using a mode-based multi-hypothesistracker, wherein the head being tracked moves across sharp boundariesrepresentative of background clutter.

FIG. 5D through FIG. 5F illustrate tracking of a human head in variousposes by a conventional non-parametric contour-based tracking schemethrough the same sequence of images illustrated in FIG. 5A through FIG.5C.

FIG. 6 illustrates an exemplary system flow diagram for using amode-based multi-hypothesis tracker to track objects.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

In the following description of the preferred embodiments of the presentinvention, reference is made to the accompanying drawings, which form apart hereof, and in which is shown by way of illustration specificembodiments in which the invention may be practiced. It is understoodthat other embodiments may be utilized and structural changes may bemade without departing from the scope of the present invention.

1.0 Exemplary Operating Environment:

FIG. 1 illustrates an example of a suitable computing system environment100 on which the invention may be implemented. The computing systemenvironment 100 is only one example of a suitable computing environmentand is not intended to suggest any limitation as to the scope of use orfunctionality of the invention. Neither should the computing environment100 be interpreted as having any dependency or requirement relating toany one or combination of components illustrated in the exemplaryoperating environment 100.

The invention is operational with numerous other general purpose orspecial purpose computing system environments or configurations.Examples of well known computing systems, environments, and/orconfigurations that may be suitable for use with the invention include,but are not limited to, personal computers, server computers, hand-held,laptop or mobile computer or communications devices such as cell phonesand PDA's, multiprocessor systems, microprocessor-based systems, set topboxes, programmable consumer electronics, network PCs, minicomputers,mainframe computers, distributed computing environments that include anyof the above systems or devices, and the like.

The invention may be described in the general context ofcomputer-executable instructions, such as program modules, beingexecuted by a computer. Generally, program modules include routines,programs, objects, components, data structures, etc., that performparticular tasks or implement particular abstract data types. Theinvention may also be practiced in distributed computing environmentswhere tasks are performed by remote processing devices that are linkedthrough a communications network. In a distributed computingenvironment, program modules may be located in both local and remotecomputer storage media including memory storage devices. With referenceto FIG. 1, an exemplary system for implementing the invention includes ageneral-purpose computing device in the form of a computer 110.

Components of computer 110 may include, but are not limited to, aprocessing unit 120, a system memory 130, and a system bus 121 thatcouples various system components including the system memory to theprocessing unit 120. The system bus 121 may be any of several types ofbus structures including a memory bus or memory controller, a peripheralbus, and a local bus using any of a variety of bus architectures. By wayof example, and not limitation, such architectures include IndustryStandard Architecture (ISA) bus, Micro Channel Architecture (MCA) bus,Enhanced ISA (EISA) bus, Video Electronics Standards Association (VESA)local bus, and Peripheral Component Interconnect (PCI) bus also known asMezzanine bus.

Computer 110 typically includes a variety of computer readable media.Computer readable media can be any available media that can be accessedby computer 110 and includes both volatile and nonvolatile media,removable and non-removable media. By way of example, and notlimitation, computer readable media may comprise computer storage mediaand communication media. Computer storage media includes volatile andnonvolatile removable and non-removable media implemented in any methodor technology for storage of information such as computer readableinstructions, data structures, program modules or other data.

Computer storage media includes, but is not limited to, RAM, ROM,EEPROM, flash memory or other memory technology, CD-ROM, digitalversatile disks (DVD) or other optical disk storage, magnetic cassettes,magnetic tape, magnetic disk storage or other magnetic storage devices,or any other medium which can be used to store the desired informationand which can be accessed by computer 110. Communication media typicallyembodies computer readable instructions, data structures, programmodules or other data in a modulated data signal such as a carrier waveor other transport mechanism and includes any information deliverymedia.

The aforementioned term “modulated data signal” means a signal that hasone or more of its characteristics set or changed in such a manner as toencode information in the signal. By way of example, and not limitation,communication media includes wired media such as a wired network ordirect-wired connection, and wireless media such as acoustic, RF,infrared and other wireless media. Combinations of any of the aboveshould also be included within the scope of computer readable media.

The system memory 130 includes computer storage media in the form ofvolatile and/or nonvolatile memory such as read only memory (ROM) 131and random access memory (RAM) 132. A basic input/output system 133(BIOS), containing the basic routines that help to transfer informationbetween elements within computer 110, such as during start-up, istypically stored in ROM 131. RAM 132 typically contains data and/orprogram modules that are immediately accessible to and/or presentlybeing operated on by processing unit 120. By way of example, and notlimitation, FIG. 1 illustrates operating system 134, applicationprograms 135, other program modules 136, and program data 137.

The computer 110 may also include other removable/non-removable,volatile/nonvolatile computer storage media. By way of example only,FIG. 1 illustrates a hard disk drive 141 that reads from or writes tonon-removable, nonvolatile magnetic media, a magnetic disk drive 151that reads from or writes to a removable, nonvolatile magnetic disk 152,and an optical disk drive 155 that reads from or writes to a removable,nonvolatile optical disk 156 such as a CD ROM or other optical media.Other removable/non-removable, volatile/nonvolatile computer storagemedia that can be used in the exemplary operating environment include,but are not limited to, magnetic tape cassettes, flash memory cards,digital versatile disks, digital video tape, solid state RAM, solidstate ROM, and the like. The hard disk drive 141 is typically connectedto the system bus 121 through a non-removable memory interface such asinterface 140, and magnetic disk drive 151 and optical disk drive 155are typically connected to the system bus 121 by a removable memoryinterface, such as interface 150.

The drives and their associated computer storage media discussed aboveand illustrated in FIG. 1, provide storage of computer readableinstructions, data structures, program modules and other data for thecomputer 110. In FIG. 1, for example, hard disk drive 141 is illustratedas storing operating system 144, application programs 145, other programmodules 146, and program data 147. Note that these components can eitherbe the same as or different from operating system 134, applicationprograms 135, other program modules 136, and program data 137. Operatingsystem 144, application programs 145, other program modules 146, andprogram data 147 are given different numbers here to illustrate that, ata minimum, they are different copies.

A user may enter commands and information into the computer 110 throughinput devices such as a keyboard 162 and pointing device 161, commonlyreferred to as a mouse, trackball or touch pad. Other input devices (notshown) may include a microphone, joystick, game pad, satellite dish,scanner, or the like. These and other input devices are often connectedto the processing unit 120 through a user input interface 160 that iscoupled to the system bus 121, but may be connected by other interfaceand bus structures, such as a parallel port, game port or a universalserial bus (USB). A monitor 191 or other type of display device is alsoconnected to the system bus 121 via an interface, such as a videointerface 190. In addition to the monitor, computers may also includeother peripheral output devices such as speakers 197 and printer 196,which may be connected through an output peripheral interface 195.

Further, the computer 110 may also include, as an input device, a camera192 (such as a digital/electronic still or video camera, orfilm/photographic scanner) capable of capturing a sequence of images193. Further, while just one camera 192 is depicted, multiple camerascould be included as input devices to the computer 110. The use ofmultiple cameras provides the capability to capture multiple views of animage simultaneously or sequentially, to capture three-dimensional ordepth images, or to capture panoramic images of a scene. The images 193from the one or more cameras 192 are input into the computer 110 via anappropriate camera interface 194. This interface is connected to thesystem bus 121, thereby allowing the images 193 to be routed to andstored in the RAM 132, or any of the other aforementioned data storagedevices associated with the computer 110. However, it is noted thatimage data can be input into the computer 110 from any of theaforementioned computer-readable media as well, without requiring theuse of a camera 192.

The computer 110 may operate in a networked environment using logicalconnections to one or more remote computers, such as a remote computer180. The remote computer 180 may be a personal computer, a server, arouter, a network PC, a peer device or other common network node, andtypically includes many or all of the elements described above relativeto the computer 110, although only a memory storage device 181 has beenillustrated in FIG. 1. The logical connections depicted in FIG. 1include a local area network (LAN) 171 and a wide area network (WAN)173, but may also include other networks. Such networking environmentsare commonplace in offices, enterprise-wide computer networks, intranetsand the Internet.

When used in a LAN networking environment, the computer 110 is connectedto the LAN 171 through a network interface or adapter 170. When used ina WAN networking environment, the computer 110 typically includes amodem 172 or other means for establishing communications over the WAN173, such as the Internet. The modem 172, which may be internal orexternal, may be connected to the system bus 121 via the user inputinterface 160, or other appropriate mechanism. In a networkedenvironment, program modules depicted relative to the computer 110, orportions thereof, may be stored in the remote memory storage device. Byway of example, and not limitation, FIG. 1 illustrates remoteapplication programs 185 as residing on memory device 181. It will beappreciated that the network connections shown are exemplary and othermeans of establishing a communications link between the computers may beused.

The exemplary operating environment having now been discussed, theremaining part of this description will be devoted to a discussion ofthe program modules and processes embodying use of a mode-basedmulti-hypothesis tracker for tracking objects of interest in one or moresequences of images.

2.0 Introduction:

The mode-based multi-hypothesis tracker described herein uses amode-based multi-hypothesis tracking (MHT) system in combination with animportance sampling function for estimating a posterior probabilitydistribution of a tracking state with respect to an image observation toprovide robust tracking of moving objects in one or more sequences ofimages. The mode-based multi-hypothesis tracker is useful for trackingobjects in complex environments, such as, for example, clutteredbackgrounds, partial occlusion, and changing lighting conditions.Further, the mode-based multi-hypothesis tracker is computationallyefficient.

The mode-based multi-hypothesis tracker is capable of tracking anyobject that can be modeled using parametric contours. For example,objects that can be modeled using parametric contours include vehicles,such as cars, aircraft, missiles, boats, etc., animals, people,including the heads, faces, arms legs, hands and fingers of thosepeople, or any other object than can be modeled using parametriccontours. It should be noted that for purposes of explanation, themode-based multi-hypothesis tracker is described herein with respect totracking of human heads and faces, but that the techniques described areequally applicable to tracking any other desired object.

Finally, it should also be noted that the following discussion uses theterms “sample” and “mode.” In the context of the following discussion,“sample” is used to denote a state space configuration obtained from aprior distribution. “Mode” is used to denote a refined “sample” thatcorresponds to a local maximum in the distribution. Note that both“sample” and “mode” represent a particular configuration of parametersin the state space.

2.1 System Overview:

The mode-based multi-hypothesis tracker, as described herein, uses modesthat are local maximums in a distribution that is refined from initialsamples in a parametric state space. Because the modes are highlyrepresentative, the mode-based multi-hypothesis tracker effectivelymodels non-linear probabilistic distributions using a small number ofhypotheses. Real-time tracking performance is achieved by using aparametric causal contour model to refine initial contours to nearbymodes. In addition, one common drawback of conventional MHT schemes,i.e., producing only maximum likelihood estimates instead of a desiredposterior probability distribution of a tracking state with respect toan image observation, is addressed by introducing an importance samplingframework into MHT, and estimating the posterior probabilitydistribution from the importance function.

In general, unlike conventional MHT schemes, the mode-basedmulti-hypothesis tracker described herein uses parametric contours,instead of object appearance, to model an object of interest. This isparticularly effective for tracking objects which can be modeled usingparametric contours, such as, for example human head and face tracking,where the head can be effectively modeled by a parametric ellipse. Whilethe head orientation and lighting can dramatically change the headappearance between image frames, the contour of the head remainsapproximately the same shape.

Further, in one embodiment, computationally efficient real-time trackingcapability is achieved through the use of a novel causal contour modelwhich avoids the necessity for iterative model refinement. Finally, thecapability to compute a posterior probability of the tracking stateX_(t) with respect an image observation Z_(t) at time t, is added to MHTby placing the MHT technique into an importance sampling framework so asto effectively estimate the desired posterior p(X_(t)|Z_(t)).

Specifically, the mode-based multi-hypothesis tracker tracks at leastone object through a sequence of images. The assumption is made that inthe first frame, the location and contour of the object or objects isknown to the mode-based multi-hypothesis tracker. In other words, a“sample” denoting a particular state space configuration obtained from aprior distribution or prediction scheme is known with respect to thefirst frame. Any of a number of conventional techniques is used tolocate the object in the initial image frame. For example, suchtechniques include edge detection, the use of color or intensitygradients, manual identification of the initial location, or any otherconventional prior distribution or prediction scheme. The mode-basedmulti-hypothesis tracker then tracks the object or objects throughoutthe remaining sequence of images in the manner described below.

Given the initial sample, a sequence of image frames is then providedfor processing by the mode-based multi-hypothesis tracker. Using thissample, the mode-based multi-hypothesis tracker then determines at leastone corresponding mode for an input image frame. In other words, giventhe initial sample, the mode-based multi-hypothesis tracker identifiesone or more “modes” that correspond to local maximums in thedistribution. Finally, after using the modes to generate an importancesampling function, and using the importance function for identifying themode having the highest estimated posterior p(X_(t)|Z_(t)), that mode isprovided as the current target estimate, and is then used as the“sample” for processing the next sequential image.

In one embodiment, given an initial sample, a number of likely modes arefirst determined or refined from an image using a conventional “activecontour technique” by performing an iterative search in a 2D imageplane. Conventional active contour techniques provide a deformablecurve, or “snake”, which moves over an image while minimizing itspotential energy. The energy of a snake can in general be divided intoan “internal energy” term constraining the overall shape of the snake,and an “external energy” function provided by the image driving thesnake towards a desired boundary. With an appropriate image energyfunction and careful initialization, an active contour snake canconverge effectively to the required boundary, thereby generating one ormore modes. Such conventional active contour techniques are well knownto those skilled in the art, and will not be discussed in further detailherein, except as they relate specifically to particular aspects of themode-based multi-hypothesis tracker.

Unfortunately, the modes returned by conventional active contourtechniques only represent maximum likelihood estimates as the activecontour technique converges on a target object boundary rather than thedesired posterior, p(X_(t)|Z_(t)). Consequently, the mode-basedmulti-hypothesis tracker described herein expands on the conventionalactive contour technique by utilizing the identified modes to generatean “importance sampling function.” Samples or “particles” are then drawnfrom the importance function. Weights for these particles are thencomputed. Finally, the weighted particles are then used for computing aposterior probability of a tracking state with respect to an imageobservation for each image frame.

While the aforementioned embodiment is useful for tracking objects, itis not necessarily efficient enough to allow for real-time objecttracking using a typical PC-type computer. Consequently, in anotherembodiment of the mode-based multi-hypothesis tracker, a 1D causalcontour model is used in place of the iterative search of the 2D imageplane to facilitate efficient sample refinement for identifying themodes for each image frame. As with the iterative search of the 2D imageplane, the use of a 1D contour model for identifying the modes for eachimage frame, is followed by the generation of an importance samplingfunction, weighting particles drawn from the importance function, andusing the weighted particles for computing a posterior probability of atracking state with respect to an image observation for each imageframe. One benefit of using the 1D causal contour model in place of theiterative search of the 2D image plane is that image processing speed inincreased to the extent where real-time object tracking is easilyfeasible on a typical PC-type computer.

Further, in still another embodiment, the robustness of the mode-basedmulti-hypothesis tracker is improved by a further refinement of thecontour model. In particular, the contour model, whether using a 2Dmodel, or the aforementioned 1D causal contour model, is further refinedby using a parametric contour as the state space so as to take domainknowledge such as a shape prior into account. Using parametric contoursin this manner serves to avoid or further reduce errors resulting frombackground distraction or discontinuities in the images. For example, inthe case of human head tracking, a parametric ellipse is used as the asthe state space. Clearly, parametric contours other than ellipses can beused, with the type of parametric contour being chosen that bestrepresents the object or objects being tracked in the images.

2.2 System Architecture:

The processes summarized above are illustrated by the general systemdiagram of FIG. 2. In particular, the system diagram of FIG. 2illustrates the interrelationships between program modules forimplementing object tracking using a mode-based multi-hypothesistracker. It should be noted that the boxes and interconnections betweenboxes that are represented by broken or dashed lines in FIG. 2 representalternate embodiments of deghosting methods described herein, and thatany or all of these alternate embodiments, as described below, may beused in combination with other alternate embodiments that are describedthroughout this document.

In particular, as illustrated by FIG. 2, a system and method for objecttracking using a mode-based multi-hypothesis tracker tracks one or moreobjects through one or more sequential image frames. To begin one ormore cameras 200 provides two or more sequential image frames 210directly to an image acquisition module 220. Alternately, the imageframes 210 are first stored to an image database or file on a computerreadable medium 210, which in turn provides the images to the imageacquisition 220 module when processing is desired.

In either case, the image acquisition module 220 then provides a currentimage frame 210 to a mode identification module 230. Initially, the modeidentification module 230 also receives an initial object tracking state240, e.g., the initial “sample” which represents the state spaceconfiguration of the object or objects being tracked in the first imageframe. As discussed in greater detail below, for processing ofsubsequent image frames 210, the mode identification module 230 receivesthe current tracking state or sample which is obtained from thepreviously analyzed image frame for processing of each subsequent imageframe. The mode identification module 230 then determines at least onemode for the current image frame 210 by using an active contour approachwhich performs an iterative search using a 2D contour model in a 2Dimage plane to identify modes that correspond to local maximums in thedistribution. As noted above, each mode represents a possible statespace configuration of the object or objects being tracked.

In another embodiment, as used in a working example of the mode-basedmulti-hypothesis tracker, the mode identification module 230 uses a 1Dcausal contour model in place of the iterative search of the 2D imageplane to facilitate efficient sample refinement for identifying themodes for each image frame. In general, the 1D causal contour modelsignificantly decreases the time needed to identify modes by restrictingcontour searching for mode identification to a set of normal lines ofthe contour of current sample with respect to the current image frame.Specific details of mode identification, using either the 2D model, orthe 1D causal contour model, are provided below in Section 3.1, and theassociated subsections.

Further, as noted above, in still another embodiment, the robustness ofthe mode-based multi-hypothesis tracker is improved by a furtherrefinement of the contour model. In particular, the contour model,whether using a 2D model, or the aforementioned 1D causal contour model,is further refined in a parametric contour module 250 by using aparametric contour which provides a shape prior for limiting thepotential deformation of the contour, thereby avoiding or limitingerroneous evolvement of the contour during the active contour search formodes. Specific details of the use of a parametric contour for limitingpotential deformations of the contour during mode identification by themode identification module 230 are provided below in Section 3.1.4.

To briefly summarize the aforementioned embodiments of the modeidentification module 230, the mode identification module identifiesmodes for the current image frame 210 using an active contour approachin one of four ways: 1) using a 2D image model; 2) using a 2D imagemodel with a parametric contour acting as a limiting shape prior; 3)using a 1D causal contour model; and 4) using a 1D causal contour modelwith a parametric contour acting as a limiting shape prior. Again,specific details of mode identification, using any of the aforementionedembodiments, are provided below in Section 3.1, and the associatedsubsections.

Once the mode identification module 230 has identified the modes for thecurrent image frame 210 using any the aforementioned alternateembodiments of the mode identification module, an importance samplingmodule 260 then uses the identified modes to generate an “importancesampling function.” The importance sampling module 260 uses a novelapplication of a conventional technique known as importance sampling toallow for the estimation of a posterior probability when using MHT fortracking objects in sequential image frames. In general, the importancesampling module 260 generates an importance function for each imageframe 210. This importance function is generated using best-fit contoursrepresenting modes within the neighborhood of a number of samples drawnfrom a prior distribution for the previous image frame 210. Next, oncethe importance function has been generated, a number of particles aredrawn from the importance function, weighted, and used to estimate aprobabilistic tracking result, e.g., p(X_(t)|Z_(t)), for the currentimage frame. Specific details of how importance sampling is applied tothe MHT tracking system are provided below in Section 3.2, and theassociated subsections.

Finally, after using the modes to generate an importance samplingfunction, and using the importance function for identifying the modehaving the highest estimated posterior p(X_(t)|Z_(t)), that a trackingstate output module 270 outputs the current target state estimate, e.g.,a “sample” for the current image frame 210. Further, the tracking stateoutput module 270 provides this “sample” to the mode identificationmodule 220 for use with the next sequential image frame 210 forprobabilistically tracking the object or objects within the nextsequential image frame as summarized above.

3.0 Operation Overview:

The system and method described herein for object tracking using amode-based multi-hypothesis tracker is applicable to tracking objects insequential images including still images, video images, scannedphotographic images, and sequential images acquired via film or digitalcameras, etc. However, for ease of explanation, the detailed descriptionprovided herein will simply address the images, however acquired, simplyas sequential images. In general, the above-described program modulesare employed in a mode-based multi-hypothesis tracker for automaticallytracking objects in two or more sequential images. This process isdepicted in the flow diagram of FIG. 6 following a detailed operationaldiscussion of exemplary methods for implementing the aforementionedprograms modules.

In general, the mode-based multi-hypothesis tracker uses an adaptationof MHT tracking which is cast in an importance sampling framework forestimating a posterior probability of a tracking state with respect toan image observation. The following sections describe in detail theoperational elements for implementing the mode-based multi-hypothesistracker using the processes summarized above.

3.1 Causal Contour Model for MHT:

As noted above, in describing the mode-based multi-hypothesis tracker,the term “sample” is used to denote a state space configuration obtainedfrom some prior distribution or prediction scheme. In addition, the term“mode” is used to denote a refined “sample” that corresponds to a localmaximum in the distribution. Note that both “sample” and “mode”represent a particular configuration of parameters in the state space.

To refine an initial contour (a sample) to the best local contour (amode), a conventional active contour technique uses a 2D contour modelto perform an iterative search for modes in a 2D image plane. However,as noted above, identification of modes using an iterative search in the2D image plane is inefficient for real-time tracking. Further, becausethe traditional active contour is non-parametric, it can easily bedistracted by background clutter, and more importantly, it is not in aready-to-use form for MHT.

Consequently, in a working example of the mode-based multi-hypothesistracker a novel a novel causal 1D contour model is used to facilitateefficient sample refinement. While in a further embodiment, a parametriccontour, such as, for example, an ellipse, is used as the state spacefor using domain knowledge such as a shape prior to avoid backgrounddistraction. These concepts are discussed in detail in the followingsections.

3.1.1 1D Contour Representation:

The basic premise of the mode-based multi-hypothesis tracker describedherein is that given a sample, it is desired to find its correspondingmode, i.e., the best contour within the vicinity of that sample.However, because of the well-known “aperture effect,” only thedeformations along the normal lines of a contour can be detected.Consequently, active contour searching can be restricted to a set ofnormal lines of the contour as illustrated in FIG. 3. Specifically, letφ, φ=1, . . . , M, be the index of the normal lines, 305 through 340,and λ, λ=−N, . . . , N, be the index of pixels along a normal line.Furthermore, let ρ_(φ)(λ) denote the image intensity at pixel λ on lineφ. In other words, ρ_(φ)(λ)=I(x_(λφ), y_(λφ)), where (x_(λφ), y_(λφ)) isthe corresponding image coordinate of pixel λ on line φ and I(x_(λφ),y_(λφ)) is the image intensity.

Each normal line, 305 through 340, has 2N+1 pixels, which are indexedfrom −N to N. The center point of each normal line is placed on theinitial contour 345 (the sample) and indexed as 0. Let c(φ) denote thebest local contour 350 (the mode) location on line φ. If all modes,c(φ), φ∈[1,M] can be detected, then the best local contour can beobtained. Note that instead of representing the contour by a 2D imagecoordinate, i.e., (x_(λφ), y_(λφ)), it is instead represented by a muchsimpler 1D function, c(φ), φ=1, . . . ,M.

3.1.3 Efficient Contour Refinement:

If the initial contour matched the best local contour exactly, thedetected contour points on all normal lines would have been exactly atthe center, i.e., c(φ)=0,∀φ∈[1,M]. However, in practice, the best localcontour c(φ) is actually located based on measurements. In thetraditional active contour scheme, this is achieved by optimizing anobjective function which favors a smooth contour along pixels havingsharp intensity changes using a slow iterative search. However, toprovide for a more efficient optimization a contour smoothnessconstraint is defined in a causal way for the objective function asdescribed below in Section 3.1.3.2. The optimal contour can therefore befound by a single iteration of dynamic programming rather than aniterative search through a 2D search plane. The objective function andthe optimization procedure are described below.

3.1.3.1 Edge Likelihood Term:

As is well known to those skilled in the art, contour points are likelyto be signified by large color or intensity changes. Consequently, edgelikelihood is chosen as a term in the objective function. The edgelikelihood is represented in energy form, which is typically referred toas the “external energy” in the parlance of active contour techniques.The edge likelihood of pixel λ on line φ, E_(e)(ρ_(φ),λ), can thereforebe computed as a function of the image gradient along the direction ofthe line: $\begin{matrix}{{E_{e}\left( \lambda_{\phi} \right)} = {{g\left( {- {{\frac{\mathbb{d}\;}{\mathbb{d}\lambda_{\phi}}{\rho_{\phi}\left( \lambda_{\phi} \right)}}}^{2}} \right)} \approx {g\left( {- \left( {{\rho_{\phi}\left( {\lambda_{\phi} + 1} \right)} - {\rho_{\phi}\left( \lambda_{\phi} \right)}} \right)^{2}} \right)}}} & {{Equation}\mspace{14mu} 1}\end{matrix}$where g(.) is an appropriate monotonically increasing function. The useof such monotonically increasing functions in an active contourtechnique are well known to those skilled in the art, and will not bediscussed in further detail herein. Assuming that the initial contour isrelatively accurate, the objective function is further refined byputting a zero-mean Gaussian kernel at the center of the normal line(see FIG. 3). Therefore, an extra energy term, which favors the edgepoints in the center part of the normal line is defined as:E _(s)(λ_(φ))=λ_(φ) ²/σ_(s) ²  Equation 2where σ_(s) controls how strong this constraint should be. For example,when the motion of the object is difficult to predict or no accuratemotion model can be obtained, the σ_(s) should be large enough toincorporate uncertainties, thereby lowering the influence of thisconstraint.

Because the above edge detection scheme only examines each normal lineindividually, it does not have enough information to ensure good overallcontour detection results in cluttered environments. Consequently, inanother embodiment, the relationship between contour points on adjacentnormal lines is taken into account. In particular, if the normal linesare relatively dense (e.g., about 20–60 normal lines were used in aworking example of the mode-based multi-hypothesis tracker) it can beseen from FIG. 3 that the best local contour points on adjacent normallines tend to have a similar amount of displacement from the initialcontour points (indexed as 0 on each normal line). Therefore, thisinter-normal-line correlation is effectively modeled by a smoothnessconstraint as described below.

3.1.3.2 Causal Smoothness Constraint:

The contour smoothness constraint has been used in many well knownconventional active contour models. It is achieved by defining an“internal energy” term to penalize the roughness of a contour. In thetraditional active contour snake model, the roughness is characterizedby the first and second derivatives of the contour. Because the firstand second derivatives of the current contour point depend on thecontour points both before and after it, this representation of thesmoothness constraint is not causal, and the best local contour can onlybe obtained iteratively. For real-time tracking of objects, it isimperative to have an efficient contour refinement process.Consequently, building on the aforementioned 1D contour model, thesmoothness constraint is defined in a causal way, thereby allowing forrapid contour refinement:E _(t)(λ_(φ−1),λ_(φ))=|λ_(φ)−λ_(φ−1)|²  Equation 3This causal definition allows for the design of a very computationallyefficient contour refinement process, as described in Section 3.1.3.3,for obtaining the best local contour in a single iteration.

Given the aforementioned constraints, the total objective function ofany given contour c(φ), φ=1, . . . ,M is defined as follows:$\begin{matrix}{{E\left( {c(\phi)} \right)} = {\sum\limits_{\phi = 0}^{M}\;\left( {{\alpha_{l}{E_{l}\left( {{c\left( {\phi - 1} \right)},{c(\phi)}} \right)}} + {\alpha_{e}{E_{e}\left( {c(\phi)} \right)}} + {\alpha_{s}{E_{s}\left( {c(\phi)} \right)}}} \right)}} & {{Equation}\mspace{14mu} 4}\end{matrix}$where α_(i), α_(e) and α_(s) are appropriate weights for each of theenergy terms. As with conventional active contour techniques, the bestlocal contour is the c(φ), φ=1, . . . ,M that gives the minimum totalenergy. Because, as noted above, on each normal line there are 2N+1locations for c(φ), a brute force approach would require (2N+1)^(M)tries before finding the best contour. However, given the aforementionedcausal definition of the smoothness constraint, it is possible to findthe best local contour efficiently by using a dynamic programming methodas described in the following section.3.1.3.3 Energy Minimization—Finding the Modes:

To obtain the best local contour (the mode) using dynamic programming,the optimization process is divided into multiple stages, starting fromφ=0 to φ=M. If the total energy (E^(o)(λ¹⁰⁰ )) of the best contourending at point λ_(φ) is known, it can be propagated to every point online (φ+1) to compute the total energy for λ_(φ+1) (E^(o)(λ_(φ+1))).This dynamic programming propagation process can be explained asfollows: $\begin{matrix}{{{E^{o}\left( \lambda_{\phi + 1} \right)} = {{\min\limits_{\lambda_{\phi} \in {\lbrack{{- N},N}\rbrack}}\left\{ {{E^{o}\left( \lambda_{\phi} \right)} + {\alpha_{i}{E_{i}\left( {\lambda_{\phi},\lambda_{\phi + 1}} \right)}}} \right\}} + {\alpha_{e}{E_{e}\left( \lambda_{\phi + 1} \right)}} + {\alpha_{s}{E_{s}\left( \lambda_{\phi + 1} \right)}}}},{\lambda_{\phi + 1} \in \left\lbrack {{- N},N} \right\rbrack}} & {{Equation}\mspace{14mu} 5}\end{matrix}$

After the energy is propagated to the last line φ=M, the best contour isobtained by first finding the minimum energy point on line M,min_(λ∈[−N,N])E^(o)(λ_(M)), and then back-tracking through all the linesto obtain the corresponding contour points on each line. Note that thisapproach reduces the computational complexity from the aforementionedbrute force approach requiring (2N+1)^(M) computations to the dynamicprogramming propagation approach which only requires (2N+1)² Mcomputations. Clearly, using the dynamic programming propagation processa massive reduction in computational complexity is achieved as Mincreases.

In summary, unlike the traditional active contour scheme, the causal 1Dcontour model allows the best contour to be obtained without iterativelysearching the 2D image plane. Note that the best contour (the mode) iswith respect to a given initial contour (the sample). Further, if twosamples are far from each other, the modes obtained can be quitedifferent, which fits perfectly into the MHT tracking framework.

3.1.4 Shape Prior—Parametric Contours:

As noted above, in another embodiment, the use of parametric contours isused to improve tracking by limiting the potential deformations of thecontour. In particular, the preceding discussion focused on embodimentswherein the tracking contour was in a non-parametric form such that eachindividual contour point can move arbitrarily, as long as the overallcontour minimizes the objective function as required by Equations 4 and5. In other words, given a non-parametric contour, the contour candeform to virtually any shape. Because of its high degree of freedom,this non-parametric representation is both susceptible to backgroundclutter and not easily used in an MHT tracking framework.

Consequently, the concept of using a parametric contour for representingthe target object of interest is added in one embodiment. Note that theparticular parametric contour which is used for modeling the targetobject of interest is dependent upon the general shape of the targetobject of interest. For example, as is well known to those skilled inthe art, because human heads are roughly elliptical regardless of thehead orientation, the human head can be effectively modeled by aparametric ellipse. Consequently, a parametric ellipse was used in aworking example of the mode-based multi-hypothesis tracker. This domainknowledge, i.e., shape prior, helps the contour to avoid erroneousevolvement, therefore greatly improving the tracking results. Thisconcept is illustrated by FIGS. 4A through 4F which illustrate trackingresults of a working example of the mode-based multi-hypothesis trackerusing a parametric ellipse as a shape prior. Note that FIGS. 4A through4F are discussed in greater detail below. Further, the use of aparametric contour, such as the parametric ellipse represents a statespace whose samples and modes can be readily used in an MHT framework.

Specifically, in the working example of the mode-based multi-hypothesistracker a five dimensional parametric ellipse was used to represent thehead contour:X=[x_(c),y_(c),α,β,Φ]  Equation 6where (x_(c),y_(c)) is the center of the ellipse, α and β are thelengths of the major and minor axes of the ellipse, and Φ is theorientation of the ellipse. Note that the initial samples are alwaysellipses. However, after the aforementioned refinement process, theidentified modes are not necessarily ellipses any more. Consequently, aleast mean square (LMS) technique is used to fit the modes to thefive-dimensional ellipse state space before producing the trackingresults.3.2 Mode-Based Multi-Hypothesis Tracking:

As noted above, one of the major limitations with conventional MHTschemes is that such schemes only produces maximum likelihood estimates,but not the desired posterior, p(X_(t)|Z_(t)). Consequently, as notedabove, the conventional MHT approach is modified by casting the MHTtracking system in an importance sampling framework in order to estimatethe posterior from MHT by using importance sampling. Construction anduse of an importance function for importance sampling is described inthe following sections. The concepts embodying importance sampling arewell known to those skilled in the art. Consequently, importancesampling will be described below only so far as to describe itsimplementation for estimating the posterior probability with respect toMHT tracking.

3.2.1 Constructing the Importance Function:

Let q be a known proposal distribution (also called the importancefunction). As is well known to those skilled in the art, it has beenproven that as I tends to infinity, the unknown posterior distribution pcan be approximated by a set of properly weighted particles drawn from aknown importance function q:$\begin{matrix}{{\hat{p}\left( {X_{t}❘Z_{t}} \right)} = {\sum\limits_{l = 1}^{I}\;{\pi_{t}^{l}{\delta_{X_{l}^{\prime}}\left( {dX}_{t} \right)}}}} & {{Equation}\mspace{14mu} 7}\end{matrix}$Where I is the number of particles, δ is the Dirac delta function, andthe weights for the particles are calculated as: $\begin{matrix}{\pi_{t}^{i} = {\frac{p\left( X_{t}^{i} \middle| X_{t - 1}^{i} \right)}{q\left( {\left. X_{t}^{i} \middle| X_{t - 1}^{i} \right.,Z_{t}} \right)} \cdot {p\left( Z_{t} \middle| X_{t}^{i} \right)}}} & {{Equation}\mspace{14mu} 8}\end{matrix}$The process of drawing particles X_(t) ^(i) from the importance functionq and calculating the particle weights π_(t) ^(i) is called importancesampling. There are an infinite number of choices for the importancefunction, as long as its support includes that of the posteriordistribution. However, when q is close to the true posterior p, theparticles are more effective. Consequently, as is known to those skilledin the art, the basic idea is to put more particles in those areas wherethe posterior may have a higher density so as to avoid relativelyuseless particles. The mode-based MHT fits into this importance samplingframework very well.

In describing the use of importance sampling as applied to MHT tracking,several terms are defined for purposes of clarity. In particular, X_(t)is used herein to denote a general state variable, as used in Equations7 and 8. Furthermore, let {overscore (X)}_(t) ^(k), k=1, . . . , K,denote the raw samples drawn from a prior distribution, and let {tildeover (X)}_(t) ^(l), I=1, . . . , L, denote the modes refined from theraw samples. Note that because of the refinement process described abovein Section 3.1.3, the best contour obtained is not necessarily anellipse, or other parametric contour. Consequently, {tilde over (X)}_(t)^(l) is used to denote the best contour after fitting the parametricellipse, (see Equation 6), or other parametric contour.

Given these definitions, modeling each mode as a local Gaussian, andusing a mixture of the modes as the importance function, q, gives:$\begin{matrix}{{q\left( {\left. X_{t}^{i} \middle| X_{t - 1}^{i} \right.,Z_{t}} \right)} \equiv {\frac{1}{L}{\sum\limits_{l = 1}^{L}{N\left( {{\overset{\sim}{X}}_{t}^{l},\sigma_{q}} \right)}}}} & {{Equation}\mspace{14mu} 9}\end{matrix}$where “≡” denotes “defined as”, and σ_(q) is the variance of theGaussian for the modes. Once the importance function q is constructed,particles {circumflex over (X)}_(t) ^(i),i=1, . . . I, are drawn fromit, and used to estimate the posterior probability by using Equations 7and 8. Note that, to preserve all the L modes in the importancefunction, the number of particles should be greater than or equal to thenumber of modes, i.e., I>=L.

Given the importance function q (Equation 9), the probability of aparticle {circumflex over (X)}_(t) ^(i) is then evaluated as:$\begin{matrix}{{q\;\left( {X_{t} = \left. {\hat{X}}_{t}^{i} \middle| {\overset{\sim}{X}}_{t}^{l} \right.} \right)} = {\frac{1}{\sqrt{2\pi}\sigma_{q}}\frac{1}{L}{\sum\limits_{l = 1}^{L}{\exp\left( {- \frac{\left( {{\hat{X}}_{t}^{i} - {\overset{\sim}{X}}_{t}^{l}} \right)^{2}}{2\sigma_{q}^{2}}} \right)}}}} & {{Equation}\mspace{20mu} 10}\end{matrix}$

Referring back to Equation 8, in order to calculate the particleweights, in addition to evaluating Equation (10), it is also necessaryto calculate the particle likelihood p(Z_(t)|{circumflex over (X)}_(t)^(i)) and the particle transition probability p({circumflex over(X)}_(t) ^(i)|{circumflex over (X)}_(t−1)). These terms are discussed inthe following two subsections.

3.2.2 Calculating the Particle Likelihood:

Let Z_(t,φ) denote the edge detection observation on line φ at time t.Because of potential background clutter, there can be multiple edgesalong each normal line. Therefore, let J be the number of detected edges(Z_(t,φ)=(Z₁, Z₂, . . . , Z_(J))). Of the J edges, at most one is thetrue contour. With the assumption that the clutter is a Poisson processalong the line with spatial density γ and the true target measurement isnormally distributed with standard deviation σ_(z), the edge likelihoodmodel is obtained as follows: $\begin{matrix}{{p\;\left( {\left. Z_{t,\phi} \middle| \lambda_{\phi} \right. = {\hat{X}}_{t,\phi}^{i}} \right)} \propto {1 + {\frac{1}{\sqrt{2\pi}\sigma_{z}q_{0}\gamma}{\sum\limits_{j = 1}^{J}{\exp\left( {- \frac{\left( {Z_{j} - \lambda_{\phi}} \right)^{2}}{2\sigma_{z}^{2}}} \right)}}}}} & {{Equation}\mspace{14mu} 11}\end{matrix}$where q₀ is the prior probability that none of the J edges is the truecontour. By assuming independence between different normal lines, thefollowing overall likelihood function is produced: $\begin{matrix}{{p\left( Z_{t} \middle| {\hat{X}}_{t}^{i} \right)} = {\prod\limits_{\phi = 1}^{M}\;{p\left( Z_{t,\phi} \middle| {\hat{X}}_{t,\phi}^{i} \right)}}} & {{Equation}\mspace{14mu} 12}\end{matrix}$3.2.3 System Dynamics and Particle Transition Probability:

As is known to those skilled in the art, the “Langevin process” can beused to model human head movement dynamics. Equation 13 provides amathematical representation of this movement model: $\begin{matrix}{\begin{bmatrix}X_{t} \\{\overset{.}{X}}_{t}\end{bmatrix} = {{\begin{bmatrix}1 & \tau \\0 & a\end{bmatrix}\begin{bmatrix}X_{t - 1} \\{\overset{.}{X}}_{t - 1}\end{bmatrix}} + {\begin{bmatrix}0 \\b\end{bmatrix}m_{t}}}} & {{Equation}\mspace{14mu} 13}\end{matrix}$where a=exp(−β_(θ)τ), b={overscore (v)}√{square root over (1−a²)}, β_(θ)is the rate constant, m_(t) is a thermal excitation process drawn fromGaussian distribution N(0, Q), τ is a discretization time step and{overscore (ν)} is a steady-state root-mean-square velocity. Assumingthat each particle forms a local Gaussian, the particle transitionprobability can then be computed as: $\begin{matrix}{{p\;\left( {\hat{X}}_{t}^{i} \middle| {\hat{X}}_{t - 1} \right)} = {\frac{1}{\sqrt{2\pi}\sigma}\frac{1}{I}{\sum\limits_{r = 1}^{I}{\exp\left( {- \frac{\left( {{\hat{X}}_{t}^{i} - {\hat{X}}_{t - 1}^{r}} \right)^{2}}{2\sigma^{2}}} \right)}}}} & {{Equation}\mspace{14mu} 14}\end{matrix}$where σ is the variance of the Gaussian kernel.3.2.4 Overall Importance Sampling Summary:

By formulating MHT in an importance sampling framework, the ability toderive the desired posterior estimates, rather than the maximumlikelihood estimates is achieved by the mode-based multi-hypothesistracker. Once cast into the importance sampling framework, the posterioris represented using the set of particles which are propagated to thenext image frame to be analyzed. Further, because the particles aredrawn from the mixture of all the modes (i.e., the importance function),the mode-based multi-hypothesis tracker is more robust thansingle-hypothesis approaches, and can recover quickly after largedistractions in the image frames. The preceding operational descriptioncan be briefly summarized as follows:

1. Generating the Importance Function:

-   -   a) Given the particle set obtained at from the image frame time        t−1, i.e., {{circumflex over (X)}_(t−1) ^(i), π_(t−1) ^(i), i=1,        . . . , I}, draw K raw samples {overscore (X)}_(t−1) ^(k), k=1,        . . . , K, from the set. Passing the raw samples through the        system dynamics model, as described in Section 3.2.3 with        respect to Equation 13, the predicted raw samples {overscore        (X)}_(t) ^(k) are obtained.    -   b) For each raw sample {overscore (X)}_(t) ^(k), find the        best-fit contour {tilde over (X)}_(t) ^(l), i.e., the mode        within its neighborhood using the dynamic mode-finding process        described above in Section 3.1.3.3. After finding the modes, the        importance function is generated using Equation 9.        2. Importance Sampling:    -   a) Draw I particles ({circumflex over (X)}_(t) ^(i), i=1, . . .        , I) from the importance function (Equation 9).    -   b) Weight the particles using Equations 8, 10, and 12.        3. Output:

Finally, once all the weights are calculated, the probabilistic trackingresult is then estimated with Equation 14 using the newly obtainedparticle set {{circumflex over (X)}_(t) ^(i), π_(t) ^(i), i=1, . . . ,I}.

3.3 System Operation:

The program modules described in Section 2.2 with reference to FIG. 2,and in view of the detailed description provided in Section 3, areemployed for automatically tracking objects in sequential image framesusing the mode-based multi-hypothesis tracker. This process is depictedin the flow diagram of FIG. 6. It should be noted that the boxes andinterconnections between boxes that are represented by broken or dashedlines in FIG. 6 represent alternate embodiments of the presentinvention, and that any or all of these alternate embodiments, asdescribed below, may be used in combination.

Referring now to FIG. 6 in combination with FIG. 2, the process can begenerally described as a mode-based tracking system which usesmulti-hypothesis tracking in combination with importance sampling forestimating a posterior probability of current target state given a priortarget state. In particular, as illustrated by FIG. 6, a system andmethod for automatically tracking an object or objects in a series ofsequential image frames begins by acquiring 600 two or more sequentialimages frames 210 using at least one camera or other imaging device 200.While the mode-based multi-hypothesis tracker is capable of real-timetracking, in one embodiment, the sequential images 210 are stored to acomputer file or database for later processing.

In either case, once at least one image has been acquired an activecontour identification process 615 uses an initial or current targetobject state or “sample” 610 along with the current image frame 605 forthe purpose of identifying one or more modes representing potentialtarget object states. As discussed above, in one embodiment, the activecontour mode identification process uses a 1D contour model 620 (seeSection 3.1.1) for identifying modes. Alternately, a 2D model is used bythe active contour mode identification process for identifying modes.

Further, in the 1D model case, a causal contour refinement process 630is used allow for mode identification in a single iteration, rather thanwith multiple iterations as is the case with conventional active contourtechniques (see Section 3.1.3). In either case, whether a 1D, or a 2Dmodel is used, in one embodiment, the identified modes 635 are fit tomodel specific parametric contours. For example, in the case of humanhead tracking, a parametric ellipse was used to model the human head. Asnoted above, the use of a parametric shape prior serves to limitpotential deformations of the mode contours, thereby reducing oreliminating evolvement errors resulting from background clutter (seeSection 3.1.4).

Next, an importance function is constructed 645 from the identifiedmodes 635 whether or not the causal contour refinement process 630 hasbeen applied to the mode contours. As described above in Section 3.2.1,this importance function uses a novel application of a conventionaltechnique known as importance sampling to allow for the estimation of aposterior probability when using MHT for tracking objects in sequentialimage frames. Note that a unique importance function is constructed 645for each image 210 frame as that image frame is processed. Once theimportance function has been generated 645, a number of particles aredrawn or extracted 650 from the importance function. These particles arethen weighted 655 and used to estimate a probabilistic tracking result,e.g., p(X_(t)|Z_(t)), for the current image frame, as described inSections 3.2.1 through 3.2.4.

Finally, after using the modes to generate the importance samplingfunction, and using the importance function for estimating modeposteriors, p(X_(t)|Z_(t)), the mode having the highest estimatedposterior is output 665 as the current target object state. In addition,if there are more image frames to process 670, then the mode having thehighest estimated posterior is provided as the new current “sample” 610in conjunction with the next sequential image frame 210 for identifyingmodes 610 in that next sequential image frame. The processes describedabove are then repeated so long as there are more sequential images toprocess 670.

4.0 Working Example:

In a simple working example of the mode-based multi-hypothesis tracker,a 1D contour model was used along with an elliptical shape prior (seeSection 3.1.4) for tracking a human head through a sequence of images.In particular, the 1D model used in this working example used 30 normallines along the ellipse contour, i.e., M=30 (See Section 3.1.1). Eachnormal line was 21 pixels long, i.e., N=10, and 20 particles were usedduring the tracking, i.e., I=20. Given these basic configurationparameters, the mode-based multi-hypothesis tracker was implemented on atypical 933 MHz PC-type computer, with the mode-based multi-hypothesistracker running at a rate of 10 frames per second.

Note that the configuration described above has no special significance.In fact, the number and length of normal lines, the number of particlesused for construction of the importance function, and the frame ratewere simply chosen as a matter of convenience. Clearly, these numberscan be increased or decreased as desired in order to address particulartracking objectives.

In this working example, a challenging real-world video sequence in acluttered environment over a large number of sequential image frames waspresented to the mode-based multi-hypothesis tracker described above.The image sequence was designed to simulate various tracking conditions,including appearance changes, quick movement, out-of-plane headrotation, shape deformation, camera zoom in and out, and partialocclusion. Referring to FIG. 4A through FIG. 4F, note that the imageframes include horizontal window blinds and a door. These blinds anddoor represent typical sharp edges and clutter that, in general, tend toimpose great challenges to visual tracking algorithms.

As noted above, the mode-based multi-hypothesis tracker is capable oftracking even with severe distractions. In fact, the use of twentyhypotheses (i.e., I=20) were found to be sufficient to successfullytrack the head throughout the sequence of images. Further, all the fiveparameters of the parametric ellipse are allowed to change. The trackingresults of the mode-based MHT approach is shown in FIG. 4A through FIG.4F as a while ellipse overlaying the face of the woman in each imageframe. Note that the mode-based multi-hypothesis tracker tracksthroughout the sequence represented by FIG. 4A through FIG. 4F. Further,in the image frames represented by FIG. 4D through FIG. 4E, themode-based multi-hypothesis tracker is distracted by partial occlusion,e.g., the tracked head is partially occluded by a second head. However,as illustrated in FIG. 4F, the correct hypothesis emerges even after thesevere distraction of the second head, and the mode-basedmulti-hypothesis tracker then resumes tracking reliably.

Furthermore, to demonstrate the importance of using the parametriccontour, a comparison of using the mode-based multi-hypothesis trackerwith a 1D model and the elliptical parametric contour was comparedagainst a conventional MHT tracking scheme with a non-parametric contourmodel. Because of the high degree of freedom in the non-parametriccontour, i.e., M=30 vs. the 5D ellipse, the local smoothness constraintsare not sufficient to assure the global shape and the contour is easilydistracted by the background clutter. For fine-level comparisonpurposes, the raw contour results are overlaid on the image frames forboth methods rather than the fitted ellipse. As shown by the distortedcontour overlaying the image frames in FIG. 5D through FIG. 5F, when theperson moves across the door from right to left, the sharp edges on theblinds and the door severely distract the conventional MHT trackingscheme with a non-parametric contour model. In contrast, as illustratedby FIGS. 5A through 5C the mode-based multi-hypothesis tracker describedabove maintains a tight contour around the persons face when trackingthe person through the exact same frames as those represented by theimages of FIG. 5D through FIG. 5F.

The foregoing description of the invention has been presented for thepurposes of illustration and description. It is not intended to beexhaustive or to limit the invention to the precise form disclosed. Manymodifications and variations are possible in light of the aboveteaching. It is intended that the scope of the invention be limited notby this detailed description, but rather by the claims appended hereto.

1. A system for tracking objects in sequential image frames comprising:acquiring at least two sequential images of a scene that includes atleast one object of interest; performing an active contour analysis ofeach sequential image frame for identifying at least one contour in eachsequential image frame which corresponds to a local maximum in adistribution of possible states for the object of interest; generatingan importance function from a sampling of the identified contours foreach sequential image frame; for each contour, using the importancefunction to estimate a posterior probability of a tracking state for theobject of interest with respect to each image frame; and identifying acontour having a highest estimated posterior probability as representinga current tracking state of the object of interest for each sequentialimage frame.
 2. The system of claim 1 wherein the sequential images areacquired from at least one camera.
 3. The system of claim 1 furthercomprising storing the acquired sequential images on a computer readablemedium.
 4. The system of claim 1 wherein the active contour analysiscomprises an iterative search of a 2D image plane using a 2D image modelfor identifying the at least one contour in each sequential image frame.5. The system of claim 4 further comprising limiting potentialdeformations of the identified contours by fitting the identifiedcontours to a parametric contour which acts as a limiting shape prior.6. The system of claim 1 wherein the active contour analysis comprisesperforming a single iteration analysis of a 1D causal contour model foridentifying the at least one contour in each sequential image frame. 7.The system of claim 6 wherein the active contour analysis of the 1Dcausal contour model comprises determining deformations along at leastone normal line of a contour representing a prior state of the object ofinterest.
 8. The system of claim 6 further comprising limiting potentialdeformations of the identified contours by fitting the identifiedcontours to a parametric contour which acts as a limiting shape prior.9. A computer-implemented process for probabilistically tracking atleast one object throughout a sequence of images, comprising using acomputer to: for each image, extract at least one contour thatrepresents a local maximum in a distribution that is refined frominitial samples in a parametric state space representing an object ofinterest in each image; refine each contour using a parametric causalcontour model; construct an importance sampling function from a samplingof the contours for each image; estimate a posterior probability of atracking state for each contour; and for each image, choosing a contourhaving a highest posterior probability as representing a current objectstate.
 10. The computer-implemented process of claim 9 whereinextracting at least one contour from each image comprises performing anactive contour search of each image given a prior object state.
 11. Thecomputer-implemented process of claim 10 wherein the active contoursearch comprises performing an iterative search of a 2D image planerepresenting the image using a 2D contour model of the object.
 12. Thecomputer-implemented process of claim 11 further comprising limitingpotential deformations of the identified contours by fitting theidentified contours to a parametric contour which acts as a limitingshape prior.
 13. The computer-implemented process of claim 10 whereinthe active contour search is performed using a 1D contour model of theobject.
 14. The computer-implemented process of claim 13 wherein theactive contour analysis of the 1D causal contour model comprisesdetermining deformations along at least one normal line of a contourrepresenting a prior state of the object.
 15. The computer-implementedprocess of claim 13 further comprising limiting potential deformationsof the identified contours by fitting the identified contours to aparametric contour which acts as a limiting shape prior.
 16. Thecomputer-implemented process of claim 9 wherein refining each contourusing a parametric causal contour model comprises using a causalsmoothness constraint to limit potential roughness of the identifiedcontours.
 17. The computer-implemented process of claim 9 furthercomprising fitting each contour to a parametric contour which is used tomodel the at least one object prior to constructing the importancesampling function from a sampling of the contours for each image.
 18. Acomputer-readable medium having computer executable instructions forusing a multi-hypothesis tracking system for automatically tracking ahuman head through at least two sequential image frames, said computerexecutable instructions comprising: using at least one camera to captureat least two sequential image frames of a scene including a human headto be tracked; providing an initial head state; using the initial headstate for performing an active contour analysis of a first image framefor identifying at least one contour that potentially represents thehuman head being tracked in the first image frame; constructing animportance sampling function from the identified contours for the firstimage frame; estimating a posterior probability of a tracking state foreach identified contour; and choosing an identified contour having ahighest posterior probability as best representing a current objectstate for the first image frame.
 19. The computer-readable medium ofclaim 18 wherein the identified contour which is chosen as bestrepresenting the current object state for the first image frame is usedin place of the initial head state in performing an active contouranalysis of a subsequent image frame for identifying at least onecontour that potentially represents the human head being tracked in thesubsequent image frame.
 20. The computer-readable medium of claim 19wherein the active contour analysis comprises an iterative search of a2D image plane using a 2D image model for identifying the at least onecontour in each sequential image frame.
 21. The computer-readable mediumof claim 20 further comprising limiting potential deformations of theidentified contours by fitting each of the identified contours to aparametric ellipse.
 22. The computer-readable medium of claim 19 whereinthe active contour analysis comprises performing a single iterationanalysis of a 1D causal contour model by determining deformations alongat least one normal line of a contour representing a prior state of thehuman head.
 23. The computer-readable medium of claim 22 furthercomprising limiting potential deformations of the identified contours byfitting each of the identified contours to a parametric ellipse.